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Fix spurious underflow exceptions for Bessel functions for ldbl-128 / ldbl-128ibm (bug 14155).

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This commit is contained in:
Joseph Myers 2013-03-16 17:50:28 +00:00
parent 6cbec759de
commit 2a185d32e8
4 changed files with 96 additions and 66 deletions
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13
ChangeLog
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@ -1,3 +1,16 @@
2013-03-16 Joseph Myers <joseph@codesourcery.com>
[BZ #14155]
* sysdeps/ieee754/ldbl-128/e_j0l.c (__ieee754_j0l): Do not compute
1 / x and functions P and Q for arguments above 0x1p256L.
(__ieee754_y0l): Likewise.
* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Likewise.
(__ieee754_y1l): Likewise.
* math/libm-test.inc (j0_test): Do not allow spurious underflows.
(j1_test): Likewise.
(y0_test): Likewise.
(y1_test): Likewise.
2013-03-16 Thomas Schwinge <thomas@codesourcery.com>
* math/test-snan.c (TEST_FUNC): Add and use minus_sNaN_var

12
math/libm-test.inc
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@ -6243,8 +6243,7 @@ j0_test (void)
TEST_f_f (j0, 0x1.d7ce3ap+107L, 2.775523647291230802651040996274861694514e-17L);
#ifndef TEST_FLOAT
/* Bug 14155: spurious exception may occur. */
TEST_f_f (j0, -0x1.001000001p+593L, -3.927269966354206207832593635798954916263e-90L, UNDERFLOW_EXCEPTION_OK);
TEST_f_f (j0, -0x1.001000001p+593L, -3.927269966354206207832593635798954916263e-90L);
#endif
END (j0);
@ -6285,8 +6284,7 @@ j1_test (void)
TEST_f_f (j1, 0x1.3ffp+74L, 1.818984347516051243459364437186082741567e-12L);
#ifndef TEST_FLOAT
/* Bug 14155: spurious exception may occur. */
TEST_f_f (j1, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L, UNDERFLOW_EXCEPTION_OK);
TEST_f_f (j1, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L);
#endif
END (j1);
@ -10457,8 +10455,7 @@ y0_test (void)
TEST_f_f (y0, 0x1.3ffp+74L, 1.818984347516051243459467456433028748678e-12L);
#ifndef TEST_FLOAT
/* Bug 14155: spurious exception may occur. */
TEST_f_f (y0, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L, UNDERFLOW_EXCEPTION_OK);
TEST_f_f (y0, 0x1.ff00000000002p+840L, 1.846591691699331493194965158699937660696e-127L);
#endif
TEST_f_f (y0, 0x1p-10L, -4.4865150767109739412411806297168793661098L);
@ -10511,8 +10508,7 @@ y1_test (void)
TEST_f_f (y1, 0x1.27e204p+99L, -8.881610148467797208469612080785210013461e-16L);
#ifndef TEST_FLOAT
/* Bug 14155: spurious exception may occur. */
TEST_f_f (y1, 0x1.001000001p+593L, 3.927269966354206207832593635798954916263e-90L, UNDERFLOW_EXCEPTION_OK);
TEST_f_f (y1, 0x1.001000001p+593L, 3.927269966354206207832593635798954916263e-90L);
#endif
TEST_f_f (y1, 0x1p-10L, -6.5190099301063115047395187618929589514382e+02L);

68
sysdeps/ieee754/ldbl-128/e_j0l.c
View File

@ -700,6 +700,25 @@ __ieee754_j0l (long double x)
return p;
}
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = s - c;
cc = s + c;
z = -__cosl (xx + xx);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
if (xx > 0x1p256L)
return ONEOSQPI * cc / __ieee754_sqrtl (xx);
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
@ -761,21 +780,6 @@ __ieee754_j0l (long double x)
p = 1.0L + z * p;
q = z * xinv * q;
q = q - 0.125L * xinv;
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = s - c;
cc = s + c;
z = -__cosl (xx + xx);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
return z;
}
@ -843,6 +847,25 @@ long double
return p;
}
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (x, &s, &c);
ss = s - c;
cc = s + c;
z = -__cosl (x + x);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
if (xx > 0x1p256L)
return ONEOSQPI * ss / __ieee754_sqrtl (x);
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
@ -904,21 +927,6 @@ long double
p = 1.0L + z * p;
q = z * xinv * q;
q = q - 0.125L * xinv;
/* X = x - pi/4
cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4)
= 1/sqrt(2) * (cos(x) + sin(x))
sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4)
= 1/sqrt(2) * (sin(x) - cos(x))
sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
cf. Fdlibm. */
__sincosl (x, &s, &c);
ss = s - c;
cc = s + c;
z = -__cosl (x + x);
if ((s * c) < 0)
cc = z / ss;
else
ss = z / cc;
z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x);
return z;
}

69
sysdeps/ieee754/ldbl-128/e_j1l.c
View File

@ -706,6 +706,29 @@ __ieee754_j1l (long double x)
return p;
}
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
if (xx > 0x1p256L)
{
z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
if (x < 0)
z = -z;
return z;
}
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
@ -767,20 +790,6 @@ __ieee754_j1l (long double x)
p = 1.0L + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
if (x < 0)
z = -z;
@ -850,6 +859,24 @@ __ieee754_y1l (long double x)
return p;
}
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
if (xx > 0x1p256L)
return ONEOSQPI * ss / __ieee754_sqrtl (xx);
xinv = 1.0L / xx;
z = xinv * xinv;
if (xinv <= 0.25)
@ -911,20 +938,6 @@ __ieee754_y1l (long double x)
p = 1.0L + z * p;
q = z * q;
q = q * xinv + 0.375L * xinv;
/* X = x - 3 pi/4
cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
= 1/sqrt(2) * (-cos(x) + sin(x))
sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
= -1/sqrt(2) * (sin(x) + cos(x))
cf. Fdlibm. */
__sincosl (xx, &s, &c);
ss = -s - c;
cc = s - c;
z = __cosl (xx + xx);
if ((s * c) > 0)
cc = z / ss;
else
ss = z / cc;
z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
return z;
}